Marx's original conception of communism wasn't a system of government, so much as it was a state of being.
He considered socialism as a necessary evil - you had government imposing the principle of "from each according to his ability, to each according to his needs", because people wouldn't do it themselves, but the idea was that as people were exposed to this, saw its benefits and became enlightened, they would start acting this way voluntarily. When the population in general had reached this state, the socialist government would become unnecessary and wither away, and the population would be living, ungoverned, as "communist man", the apex of Marx's conception of social evolution.
Unfortunately, this breaks down, because the great benefits of socialism turn out to be mass starvation and poverty, which the people understandably get miffed about and don't embrace, which leads to their government shooting them in job lots. It's also why a lot of Marxists complain that communism has never really been implemented yet, and use that as a defence against the butchery their philosophy leads to.